Quantifying uncertainty in parameter estimates of ultrasonic inspection system using Bayesian computational framework

This paper will aim to characterise statistically the uncertain parameters in an ultrasonic (UT) inspection system from limited signal measurements and prior information in order to enhance the confidence on the probability of detection (POD) curve. The POD curve is widely used in industry to quantify the capability of a non-destructive testing technique to detect a defect with a given specifications. A realistic estimation of the POD requires to consider the uncertainty in the input parameters. However, in practice the uncertainties are seldom well quantified, which may cause problems for the POD estimation and its reliability to qualify robustly an inspection system. To address this issue, one proposes to characterise the uncertain parameters based on the information content in the UT signal. One of its distinctive features which can be used to solve the challenging inverse problem is the amplitude of the signal. A Bayesian approach seems a convenient framework for coping with limited number of measurements and prior information from experts' judgement to keep POD cost as low as possible. An illustration which consists to control a tube with an embedded defect is provided to demonstrate the efficiency of the proposed methodology to quantify uncertainty in the input parameters. The nested sampling (NS) algorithm is used to make Bayesian inference for an efficient exploration of the posterior space. To reduce the computational requirements, the UT physical model is replaced by an emulator based on the least square support vector machines method. The obtained results show that by combining a limited number of measurements with priors may be a promising way to characterise statistically the uncertain parameters within reasonable computational time and acceptable accuracy. The study is carried out numerically by exploiting synthetic data generated from an UT physical model.